Stability of Nonlinear Systems with Parameter Uncertainty

Engineered systems, such as power systems, naturally experience disruptions to normal operation.  Whether a system is able to recover from a particular nonlinear disturbance depends on the values of system parameters, which are typically uncertain and time-varying.

The goal is to numerically determine the boundary in parameter space, called the recovery boundary, between parameter values which lead to recovery and those which lead to a failure to recover to an initial stable equilibrium point.  Two classes of theoretically motivated algorithms are developed to compute values on the recovery boundary.

To justify these algorithms, it is first necessary to prove continuity of the region of attraction boundary under parameter perturbations for a large class of nonlinear systems.  Then, it is shown that varying parameter values so as to maximize the time the trajectory spends in a neighborhood of a special equilibrium point, or to maximize the norm of the trajectory sensitivities, drives the parameter  values to the recovery boundary.

This theory motivates the transformation of the abstract problem of computing the recovery boundary into concrete numerical optimization algorithms.  These algorithms are applied to assess fault vulnerability in power systems, and reveal unexpected dynamic behavior that would not have been observed otherwise.

Chair: Professor Ian Hiskens